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Photoevaporating Flows from the Cometary Knots in the Helix Nebula (NGC 7293)

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Photoevaporating Flows from the Cometary Knots in the Helix Nebula (NGC 7293) DRAFT VERSION OCTOBER 29, 2018 Preprint typeset using LATEX style emulateapj v. 04/03/99 PHOTOEVAPORATING FLOWS FROM THE COMETARY KNOTS IN THE HELIX NEBULA (NGC 7293) a aPARTIALLY BASED ON OBSERVATIONS MADE WITH THE NASA/ESA HUBBLE SPACE TELESCOPE, OBTAINED FROM THE DATA ARCHIVE AT THE SPACE TELESCOPE SCIENCE INSTITUTE. L. LÓPEZ-MARTÍN1,A.C.RAGA1,G.MELLEMA2,W.J.HENNEY3,J.CANTÓ1 Draft version October 29, 2018 ABSTRACT We explain the Hα emission of the cometary knots in the Helix Nebula (NGC 7293) with an analytical model that describes the emission of the head of the globules as a photoevaporatedflow produced by the incident ionizing radiation of the central star. We compare these models with the Hα emission obtained from the HST (Hubble Space Telescope) archivalimages of the Helix Nebula. From a comparisonof theHα emission with the predictions of the analytical model we obtain a rate of ionizing photons from the central star of about 5 × 1045 s−1, which is consistent with estimates based on the total Hβ flux of the nebula. We also model the tails of the cometary knots as a photoevaporated wind from a neutral shadow region produced by the diffuse ionizing photon field of the nebula. A comparison with the HST images allows us to obtain a direct determination of the value of the diffuse ionizing flux. We compare the ratio of diffuse to direct stellar flux as a function of radius inside an HII region with those obtained from the observational data through the analytical tail and head wind model. The agreement of this model with the values determined from the observations of the knots is excellent. Subject headings: ISM: structure — planetary nebulae: individual (NGC 7293) — stars: AGB and post-AGB 1. INTRODUCTION low luminosity of the star also implies a very low density wind, making it virtually undetectable. However, with its expected The small scale structure of the Planetary Nebula (PN) ≃ −1 known as the Helix Nebula (NGC 7293, PK 36-57◦1) is charac- high velocity (v∞ 6000 km s if radiation driven) it could still have a dynamical effect on the PN structure. terized by many thousands of small knots. These knots (which The measured densities in the nebula are low, about 60 cm−3 were first reported by Vorontsov–Velyaminov 1968) have a cometary shape, with their tails pointing away from the cen- (O’Dell 1998), in contrast with the densities derived for the neutral/molecular globules, n ∼ 106 cm−3 (O’Dell & Han- tral source. Groundbased work (Meaburn et al. 1992, 1996, knot dron 1996). This leads to the curious result that a substantial 1998) and Wide Field and Planetary Camera HST observations (O’Dell & Handron 1996; O’Dell & Burkert 1997; Burkert & fraction of the mass of the PN is in the form of these neutral globules. The aspherical shape of the PN is also found in the O’Dell 1998) revealed a multitude of spatially resolved knots, about 3500, with highly symmetric appearance. The knots have distribution of the knots and in the large scale CO emission. also been detected in CO (Hugginset al. 1992) and, at least out- Meaburn et al. (1998) have shown that the knots follow the same velocity distribution as the CO, although at a lower typical side the main nebula, in C I (Young et al. 1997). This PN is one of the closest to us with a parallax distance of expansion velocity. Young et al. (1999) found the deprojected 213 pc (Harris et al. 1997). Other methods have been applied to expansion velocities of the knots and the CO ring to be 19 and 29 kms−1, respectively. arXiv:astro-ph/0010026v1 2 Oct 2000 determine the distance to this PN, giving values ranging from 120 to 400 pc. Optical images show a complicated morphol- Some other authors have treated the photoevaporation of clumps in an ionizing radiation field. Bertoldi & McKee (1990) ogy characterized by a helical structure in Hα and [N II] and a developed an approximate analytic theory of the evolution ofa more elliptical shape in [O III]. The deprojection of these im- ages has proven to be difficult, with suggestions of both ellipti- photoevaporating cloud exposed to the ionizing radiation of a cal/toroidal shapes and bipolar ones (Meaburn & White 1982) newly formed star, finding an equilibrium cometary cloud con- figuration. Johnstone, Hollenbach & Bally (1998) modelled being made. O’Dell (1998) has suggested that the ionized re- gion is a disk. the photoevaporation of dense clumps of gas by an external The central star is very hot and has a low luminosity, indi- source of ultraviolet radiation including thermal and dynami- cal effects. Mellema et al. (1998) study the evolution of dense cating that it is well down the cooling track of its post-AGB evolution. The temperature of the central star of the Helix has neutral clumps located in the outer parts of a planetary nebula (like the Helix nebula). been measured by the Hβ Zanstra method to be ≃ 1.2 × 105 K (Górny, Stasinska´ & Tylenda 1997). 2. ANALYTICAL MODEL FOR THE PHOTOEVAPORATED FLUX OF The high effective temperature combined with the fairly low THE COMETARY KNOTS luminosity and the large size of the PN , about 0.5 pc in diam- eter at a distance of 213 pc, leads to a complicated ionization Let us discuss a simple, analytical model for cometary knots structure with co-existing regions of high and low ionization embedded in a Planetary Nebula (PN). First, we derive some character (O’Dell 1998; Henry, Kwitter & Dufour 1999). The expressions that relate the ionizing stellar flux and the particle flux of the photoevaporated wind in a similar way to Mellema 1Instituto de Astronomía, UNAM, Apdo. Postal 70-264, 04510 México, D. F., México 2Stockholm Observatory, S-133 36 Saltsjöbaden, Sweden 3Instituto de Astronomía, UNAM, J. J. Tablada 1006, Colonia Lomas de Santa María, 58090 Morelia, Michoacán, México 1 2 PhotoevaporatingflowsfromthecometaryknotsintheHelix nebula (NGC 7293) θ Rh F * n h F h h FIG. 1.— Schematic diagram of the cometary head. Fh is the incident flux at the surface of the neutral knot, and Rh and nh are the radius and the density of the neutral knot (respectively). et al. (1998) to find the Hα emission for the cometary heads. + 2 Cantó et al. (1998) proposed the idea of the tails as neutral F⋆ cos(θ) ≃ Fh(θ) hnh(θ) αB , (3) shadow regions behind the clumps, and studied the complex time-evolution of the resulting flow. In this paper, we model the where αB is the case B recombination coefficient of hydrogen, tails behind the Helix clumps as a cylinder of neutral material which is assumed to be constant with position. The flow thick- being photoionized by the diffuse ionizing flux of the nebula. ness h is defined by : h ≡ R (4) 2.1. A model for the cometary head ω h , Let us consider the problem of a hemispherical, neutral knot where the parameter ω is defined through the relation : of radius Rh which is being photoionized by the radiative field ∞ 2 2 emitted by the central star of the ionized nebula. A schematic ω nh Rh ≡ n (r) dr . (5) diagram of this configuration is shown in Figure 1. ZRh A fraction of the stellar flux arrives at the knot surface, pho- This parameter ω depends on the density profile of the photo- toionizing the neutral knot material and feeding a photoevapo- evaporated wind. For a D-critical ionization front (v(Rh)= ci, rated flow. The remaining ionizing photons are absorbed in this where ci is the isothermal sound speed of the ionized gas), photoevaporated flow. The neutral knot is being photoevapo- ω ≃ 0.1 (Henney & Arthur 1998). From equations (1-5) we rated, but we consider a quasi-steady state in which the radius then obtain a relation between the ionizing flux from the cen- of the knot Rh is almost constant with time. The incident flux at tral star F⋆, and the incident flux at the knot surface Fh(θ) : the knot surface is : R ≃ + 2 ω h αB F⋆ cos(θ) Fh(θ) Fh (θ) 2 , (6) Fh(θ)= nh(θ) v(Rh), (1) ci where Fh is the flux of ionizing photons incident normal to the The term on the left is the ionizingstellar flux as a functionof knot surface (per unit area and time), nh and v(Rh) are the den- the angle of incidence, the first term on the right is the incident sity and the velocity of the photoevaporated wind at the knot ionizing flux on the knot surface that produces the photoion- surface . We note that the rate of photoionizations depends izations of the neutral material and the second term is the flux on the angle of incidence θ (see Figure 1), having a maximum absorbed in the photoevaporated wind. If we define : value in the front of the cometary head. 2 In order to obtain the density profile, we consider the conser- ci ξh ≡ , (7) vation of particles in the photoevaporated wind : Rh ω αB equation (6) can be written as : 2 2 R n(R,θ)v(R)= Rhnh(θ)v(Rh), (2) 2 Fh (θ) where R is the radius directed outwards from the knot. F⋆ cos(θ) ≃ Fh(θ) + , (8) We assume that the ionization front is thin compared with the ξh effective thickness h of the ionized flow and that h in turn is We can see from equation (8) that it is possible to find the small compared with Rh. In this case, if all diffuse photons are incident flux Fh(θ) as a function of the ionizing flux F⋆ solving absorbed “on-the-spot”, the photoionization balance is given by the quadratic equation to obtain : López-Martín et al.
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